# How do you find an angle with a positive measure and an angle with a negative measure that are coterminal with 50^circ?

Feb 17, 2018

${A}_{c} = A + k \times {360}^{o}$
${A}_{c} = 50 + {360}^{o} = {410}^{o}$ (or ${50}^{o}$) and
${A}_{c} = 50 - {360}^{o} = - {310}^{o}$

#### Explanation:

Coterminal angles ${A}_{c}$ to angle A may be obtained by adding or subtracting $k \times 360$ degrees or $k \times \left(2 \Pi\right)$. Hence,

${A}_{c} = A + k \times {360}^{o}$ if A is given in degrees.

or

${A}_{c} = A + k \times \left(2 \pi\right)$ if A is given in radians.

where k is any negative or positive integer.

A couple of good tutorials are here:
http://www.analyzemath.com/Angle/coterminal_angle.html

http://www.mathwarehouse.com/coterminal-angle/how-to-calculate-coterminal-angles.php